The SR-EV model for chromatin is derived from the Self Returning Random Walk (SRRW) model that was recently introduced by this group (Huang et al., 2020). Here, we review the SRRW model and then we introduce the modifications that lead to the SR-EV model.

The SRRW model is essentially a random walk with specific rules introduced to capture statistical features of chromatin organization as revealed by experiments. At each step in the SRRW generation there are two possibilities: (1) Perform a forward jump or (2) Return over the previous step to the previous position. The probability PR for a return step is given by(1)PR(U0)=U0−αα

Here, U0 is the length of the last step along the backbone over which the walk may return. The folding parameter α>1 controls the number of returns. If the SRRW does not continue with a return step, it must continue with a forward jump. The new forward jump is chosen with an random direction and with a length U₁ given by the following probability distribution function (pdf)(2)PJ(U1>1)=α+1U1α+2

We will generally refer to Equations 1 and 2 as the return rules of the SR-EV model. There is a minimum size for the forward jumps that also defines the unit of length in the model. The succession of forward jumps and return steps leads to a structure than can be regarded as a linear backbone with tree-like branches along its length, with the branching points representing overlaps created by the return steps. In addition to the return probability and pdf defined above, the SRRW generation algorithm (contained in Appendix 1) includes a local cutoff to avoid unrealistically long steps and a spherical global cutoff to contain the configuration. The global cutoff is applied during the generation of the conformation and is measured from the center of mass of the already-generated steps.

By construction, since the SRRW includes returns over the previous steps, it contains a large number of overlaps. For α = 1.10, 1.15, and 1.20 the number of returns is 48.7%, 47.5%, and 46.2% of the total number of steps, respectively. Therefore, as a representation of a physical system, such as chromatin, the SRRW has two important drawbacks: (1) the conformations violate the principle of excluded volume and (2) it is not a linear polymer. In order to recover these two physical properties we extended the SRRW to develop the SR-EV model. In this new method, the overlapping points are transformed into connected clusters of beads that explicitly represent a linear chain, as shown on the scheme displayed in Figure 1. The method that we employ to remove overlaps is a low-temperature-controlled molecular dynamics simulation using a soft repulsive interaction potential between initially overlapping beads, that is terminated as soon as all overlaps have been resolved, as described in the Appendix 1. An example of an SRRW configuration and its corresponding SR-EV are displayed in Figure 2A and E, respectively. Figure 2B, F represents a small region on the periphery of the configuration and exemplifies how structures formed by a sequence of forward and returns steps expands to a larger cluster after including excluded volume interactions. The porosity of the structure is also affected by the excluded volume introduced in SR-EV.

The density heterogeneity displayed by the SR-EV configurations can be analyzed in terms of the accessibility. One way to reveal this accessibility is by calculating the coordinations number (CN) for each nucleosome, using a coordination radius of 11.5 nm, along the SR-EV configuration. CN values range from 0 for an isolated nucleosome to 12 for a nucleosome immersed in a packing domain. In Figure 3, we show the SR-EV configuration shown in Figure 2, but colored according to CN. CN can be also considered as a measure to discriminate heterochromatin (red) and euchromatin (blue). Figure 3A shows how the density inhomogeneity is coupled to different CN, with high CN represented in red and low CN represented in blue. Figure 3B shows a 50-nm thick slab obtained from the same configuration that clearly shows the nucleosomes at the center of each packing domain are almost completely inaccesible, while those outside are open and accessible. It is also clear that the surface of the packing domains is characterized by nearly white nucleosomes, i.e. coordinated toward the center of the domain and open in the opposite direction.

For this work, we adopted a unit length of 10 nm, similar to the diameter of a nucleosome (Maeshima et al., 2014). Therefore, each bead of the model chromatin represents a nucleosome. The spherical global cutoff was set to Rc= 650 nm. From the resulting conformations, we can cut slabs spanning well over 1 µm in cross section. Excluded volume was introduced by imposing a non-overlap radius of r∘=4.9 nm between all the beads of the SR-EV model. With these quantities, we defined the overall average volume fraction as ϕ=N(r∘/Rc)3, with N the number of beads in the chromatin model chain. We considered four different volume fractions ϕ= 0.08, 0.12, 0.16, and 0.20, which correspond to N= 186,741, 280,112, 373,483, and 466,854, respectively. Each one of these four average volume fractions was studied with three different folding parameters α= 1.10, 1.15, and 1.20. SR-EV configurations, as we present them in this work, are associated to the structure of a single chromosome. Therefore, all the analysis that follows is done on the structure of a single chromosome system. For each combination of ϕ and α, we created an ensemble of 1000 different chromatin configurations. In order to introduce the genomic distance along the SR-EV configuration we assign 147 base pairs to each nucleosome, representing the length of DNA wrapping the histone octamers. Considering that the effective bead diameter is 9.8 nm, the average distance between adjacent base pairs in the DNA double helix, and the model bonds Ui that are larger than 10 nm, we assign the number of base pairs in the linker DNA as the nearest integer of (Ui−9.8nm)/(0.34nm). In Table 1, we summarize the 12 studied cases with the resulting mean value for the length, in base pairs, of the linker DNA between nucleosomes that slightly depends on ϕ and α. The overall average length of the linker DNA sections is 39.6 base pairs and with values of 36.3 and 44.4 for the two extreme cases. We must remark that the predicted DNA length between histone octamers agrees with the widely reported values (Beshnova et al., 2014; Wang et al., 2021; Lequieu et al., 2019; Li et al., 2023; Zhurkin and Norouzi, 2021). Finally, and in order to correlate our work with experimental examples, the longest simulated chromatin corresponds to 88×106 base pairs, which is approximately the size of human chromosome 16.

In order to start assessing whether the SR-EV model produces realistic configurations of chromatin it is necessary to bring the model to a representation similar to the results of imaging experiments. For example, ChromSTEM captures the chromatin density from a slab of 100 nm thickness. Then, we cut a similar slab from an SR-EV configuration and transform the point coordinates of the model nucleosomes to a two dimensional density that considers the nucleosomes volume. In Figure 4A, we show a representation of an SR-EV configuration as it result from the model and in Figure 4B the collapsed two dimensional density as a colormap highlighting the porosity of the model and the emergence of chromatin packing domains. In Figure 4C, we show a ChromSTEM image for A549 cell. Since our SR-EV structures represent a single chromosome, it does not cover the full field of view of 1300 nm × 1300 nm that can be appreciated in the experimental image. However, the qualitative resemblance of the theoretical and experimental chromatin densities is stunning. The quantitative characterization of the model and its agreement with experimental results is analyzed below.

SR-EV is a non-homogeneous polymer model. The only physical interactions present in the model are the connectivity, the excluded volume, and the confinement that, together with the return rules induce the formation of granular structures, or packing domains, with local density variations. This granularity can be qualitatively visualized by wrapping a mesh around the chromatin conformation, as shown in Figure 2G, H. Rotating versions of Figure 2G, H are included in Figure 2—video 1 and Figure 2—video 2. It is worth noting that this representation is qualitatively similar to Figure 4, panels E, F, and G from Ou et al., 2017. At first glance, the wrapping interface between the region denser in chromatin and the region almost empty of chromatin resembles the dividing interface between two disordered bi-continuous liquid phases (Walker et al., 2014). We find this outcome from the SR-EV model quite interesting in view of recent claims that liquid–liquid phase separation could be related to heterochromatin and euchromatin segregation, and that chromatin domains have a liquid character (Chen et al., 2022; Itoh et al., 2021). Moreover, the bi-continuous topology offers two important functional advantages: First, the interface offers a very large surface area exposing the a significant fraction of the genome and second, the continuity of the dilute phase allows for the migration of free crowders (including proteins, transcription agents, mRNA, etc.) to any region in the nucleus.

The granularity of chromatin manifest itself in the polymeric properties of the model. Chromatin is a special type of polymer, and requires a careful analysis. The scaling relationship between the end-to-end distance and the polymer contour length, in this case the genomic distance, cannot be described in general with a single power-law relationship, i.e. a single Flory exponent, as it is the case for synthetic polymers. In Figure 5A, we display the ensemble averaged end-to-end distance, ⟨R2(n)⟩0.5 as a function of the genomic distance n. All the studied cases are included in the plot, but they coalesce in three distinct groups according to the folding parameter α and with almost no effect of the overall volume fraction. The figure also shows a transition occurring for n∼4×104 base pairs, from a local or intra-domain regime that corresponds with distances up to 100 nm, to a long-range or inter-domain one. The Flory exponent in the intra-domain regime (0.342, 0.347, and 0.354 for α=1.10, 1.15, and 1.20, respectively) is consistent with a nearly space-filling cluster and slightly smaller than in the inter-domain regime (0.353, 0.394, and 0.396). For n values larger than 10⁶ the curves level off due to the effect of the spherical confinement. The analysis can also be applied to the ensemble average contact probability, ⟨Cp(n)⟩, which is defined as the probability for two base pairs, separated along the polymer by a genomic distance n, of being in contact with each other (or being at a distance smaller than a cutoff). In Figure 5B, we display ⟨Cp(n)⟩ for all studied cases, using a cutoff distance of 35 nm. We see in this figure that the contact curves depend only marginally on volume fraction as the four distinct cases for each α are nearly indistinguishable. Thus, this indicates that measures of connectivity observed in Hi-C would not depend on nuclear volume concentrations. This finding is in strong agreement with the results reported in Liu and Dekker, 2022 where expansion and contraction of isolated nuclei has minimal effects on contact scaling, S. As in the end-to-end distance, in ⟨Cp(n)⟩ we can also distinguish a transition between intra- and inter-domain regimes. In general, the slope S of ⟨Cp(n)⟩ in log–log representation is larger than −1 in the inter-domain regime, and fluctuate around −1 for inter-domain genomic distances. Figure 5C shows the contact probability determined from Hi-C experiments. The blue dots correspond to chromosome 1 of HCT-116 cells and the behavior between 10⁵ and 10⁶ base pairs is well described by a slope S very close to −1. The experimental data also show a change at intermediate separations. It is important to note to the agreement is relatively good even in quantitative terms, with the transition occurring at similar genomic distance and value of Cp(n). Since the model does not have a genomic identity or any specific architectural modifiers (e.g. CTCF(CCCTC-binding factor) and/or cohesin), the contact probability curves do not represent a particular cell or chromosome. We must mention that the other chromosomes from the HCT-116 cells have a qualitatively similar contact probability, with a power-law fitting having slopes S varying from −0.85 to −1.10, depending the case.

The heterogeneous character of chromatin revealed by experiments is captured, as we have qualitatively shown above, by the SR-EV model. A straightforward characterization of this heterogeneity is the distribution of local volume fraction calculated with a probing volume of adequate size. In the language common in chromatin experiments, this volume fraction is referred to as the chromatin volume concentration (CVC) and the probing volume is, for example, a cube with an edge of 120 nm. Using electron microscopy and tomography techniques (ChromEMT), the group of Dr Clodagh O’Shea (Ou et al., 2017) reconstructed the conformation of chromatin on a 120-nm thick slab with an area of 963 nm × 963 nm, which allowed them to measure the CVC distribution using a 8 × 8 × 1 grid with cubic cells of 120 nm edge size. To calculate the CVC from the SR-EV configuration ensembles we followed the same methodology employed in the experiments. Since we have the full 3D structure of the model chromatin we are not restricted to a slab, then we used a 6 × 6 × 6 cubic grid of (120 nm)³ probing volumes. Moreover, our results represent ensemble averages over the populations of 1000 replicates for each of the Φ and α combinations. The results for each case are summarized in Figure 6 revealing that both SR-EV parameters, Φ and α, are important in determining the CVC distributions. We see that overall the volume fraction take values up to 0.6, which is consistent with our model representing the nucleosomes as spheres that can achieve a maximum volume fraction of 0.74 as a crystal and 0.64 in the jamming limit (Jin and Yoshino, 2021). The peak of the CVC distribution increases as the overall volume fraction α increases. The recent ChromEMT results reveal a CVC distribution covering a nearly identical range to our SR-EV results. Comparing with the experimental results, for the lowest overall volume fraction the distribution has an excessive proportion of low-density regions. Consequently, although we show that all regimes will result in domain formation with α=1.15 and ϕ=0.16 being the closest to what is observed in A549 cells (Figure 7C), this would indicate that the variation in chromatin density that arises in mammalian cells would be predicted to have distinct functional consequences that would not be captured by connectivity. As we show below, chromatin packing domain organization will be weakly and inversely related to the probability of return events but strongly associated with the local volume concentrations.

Since the CVC is a measure using a relative large probing volume its distribution with values ranging from 0 to 0.6 may be achieved by a (dynamic) smooth continuous modulation of the chromatin density or by a (also dynamic) mixing of distinct high- and low-density regions. The latter scheme gives rise to the concept of packing domains, as it has been recently proposed from the analysis of imaging experiments (Li et al., 2022; Li et al., 2021; Miron et al., 2020). The formation of domains is also consistent with the possibility of a microphase separation process dynamically occurring in chromatin (Strom et al., 2017; Larson et al., 2017; Falk et al., 2019; Hilbert et al., 2021). Moreover, a dynamic disordered bi-continuous phase separation is also in line with all the mentioned scenarios, especially considering that all imaging experiments are restricted to a quasi 2D slab of the system that could be insufficient to reveal a full 3D topology.

For the analysis of the SR-EV configurations, we take advantage of the methodology developed by our experimental collaborators and transform our coordinates to a stack of images (Li et al., 2022; Li et al., 2021). For this transformation, each bead is represented by a normal distribution and its contribution to a given voxel of the tomogram is the integral of the normal distribution over the voxel volume. We include Figure 4—video 1 that is an example of the resulting volumetric image stack. As we display in Figure 4B, the image representation of the SR-EV conformations immediately reveals, in 2D, the inhomogeneity of the chromatin density that includes multiple regions of high density that we identify as packing domains. We analyzed the distribution of packing domain radii using the procedure outlined in Figure 7—figure supplements 1 and 2, which is essentially the same as the experimental one. In Figure 7A, we display the distribution of domain radii for all simulated conditions and the mean value for the 12 cases is displayed in Figure 7B. For comparison, we include in Figure 7C the results from our experiments on an A549 cell line (Li et al., 2022) obtained with ChromSTEM that agree very well with the theoretical values in general, and in particular the agreement is excellent with the case corresponding to α=1.15 and ϕ=0.16.

In order to further characterize the structure of the model chromatin we calculated the pair correlation function between the model nucleosomes, i.e. g(r). From the model definition and previous analysis, we know that g(r) must reveal different features at different length scales. At short distances, r≲ 40 nm, g(r) shows the structure of the dense packing domains through the typical maxima and minima, at the intermediate distances corresponding to the average size of the packing domains and the transition between intra- and inter-domains g(r) is a decreasing function of r approaching the expected plateau for large distances. Motivated by the mass scaling analysis introduced in ChromSTEM experiments (Li et al., 2022; Li et al., 2021) we will use the integral form of the pair correlation function: G(r)=∫0r4πr′2g(r′)dr′. G(r) smoothes out the short distance oscillations of g(r) and reflects the intermediate regime as a power law with exponent D< 3.

In Figure 8A, we show in a log–log representation, as an example, the ensemble average ⟨G(r)⟩ corresponding to the global volume fraction ϕ=0.16 and the three values of α. Between 40 and 120 nm we found that the ⟨G(r)⟩ is essentially a perfect straight line, i.e. ⟨G(r)⟩∝rD. We define D as the packing parameter that we calculate for 40 <r/nm< 120. The slopes for the three displayed cases are slightly different, with D values ranging between 2.75 and 2.80 as α decreases from 1.20 to 1.10. In Figure 8B, we summarize the results for D for all the simulated conditions, which shows that D has a positive correlation with ϕ, the overall volume fraction of the whole configuration, and a weaker inverse dependence on the folding parameter α.

A similar power-law regression can be applied on the Gi(r) obtained for each configuration. We use the subscript i to distinguish that the quantity corresponds to a single configuration i. Since the configurations are obtained using a stochastic procedure, there is a large variability in the power-law fits obtained from them and some examples are included in Figure 8—figure supplement 1. In Figure 8C, we show the distributions of Di values for all 12 simulated conditions. Notice that individual Di can be larger than 3. To understand this in the context of population heterogeneity of chromatin structure, we performed live-cell PWS microscopy on U2OS cells and measured the distribution of chromatin packing states observed. As demonstrated from SR-EV, variations packing arise from the same α and ϕ conditions due to the probabilistic nature of the model. Consequently, this demonstrates that population heterogeneity arises intrinsically from our model, a finding consistent with experimental results (Figure 8C). This heterogeneity arises in simulated conditions and is in best agreement for U2OS cells in the condition of α of 1.15 and ϕ of 0.16.

Up to this point, we have performed our analysis based on the SR-EV parameters α and to distinguish the different ensembles of configurations. However, the local volume fraction, as it has been shown in Figures 2 and 6, fluctuates at the scale of the packing domain size. This inhomogeneity makes the representation of a configuration by its overall SR-EV parameter ϕ not completely meaningful when we study a local or mesoscopic property, such as the packing parameter Di. Therefore, it is convenient to introduce the local average chromatin volume fraction ⟨ϕi⟩ calculated in exactly the same 240 nm sphere that we use to calculate Di. The correlation between these two mesoscopic quantities is plotted in Figure 9 and includes every one of the SR-EV 12,000 configurations. There is a very clear and interesting correlation between Di and ⟨ϕi⟩. For high ⟨ϕi⟩, the local Di approaches to 3, which is the theoretical upper limit for ⟨D⟩. For intermediate and small ⟨ϕi⟩, there is a quite wide distribution of Di values, consistent with the violin plots of Figure 8C. Nevertheless, the local chromatin volume fraction is the main factor determining the corresponding packing parameter. In the next portion, we will demonstrate the predictions of SR-EV by affecting the probability of returns and the contribution of excluded volume by depleting RAD21 in HCT-116 cells.

So far, we have presented the integration of α with excluded volume effects on representative, and distinct, methods to measure chromatin structure (Hi-C, live-cell PWS microscopy, and ChromSTEM). It is evident from SR-EV that these methods probe different features of genomic organization, which using SR-EV, could potentially be converged. To test the role of α in the regulation of genome structure, we target processes that govern stochastic returns. Recent work has demonstrated that cohesin-mediated loops are short lived, with an individual loop existing in that configuration ∼6 % of the time (Gabriele et al., 2022). Likewise, the process of forming long-range returns is not exclusive to cohesin loop extrusion and arises from the confinement of a polymer in a crowded space as well as from transcription-induced promoter–promoter or promoter–enhancer interactions. Thus, even in the absence of cohesin or transcription, entropic loops would exist in chromatin. Consequently, all of these processes converge as components that produce a probability of a long-range step with a reciprocal probability of return at each individual loci across any individual cell. The returns and forward steps exist on a monomer scaffold and therefore individual nucleosome monomers cannot overlap in the same space.

Quantitively, SR-EV models the loss of cohesin-mediated loops as a decrease in α (e.g. from 1.20 to 1.15 or 1.10) without a change in nuclear volume at short-time scales (ϕ remains constant). SR-EV predicts (1) that domains will still exist on ChromSTEM (Figure 7A), (2) there will be a ∼20% decrease in the number of domains, (3) the remaining domains will have similar sizes, densities, and mass scaling (Figure 8C), (4) population heterogeneity would be largely unaffected, and (5) D in each domain will be predominantly determined by the local volume fractions (Figures 8B and 9). This view is in contrast to an alternative polymer model that produces biphasic structures from attractions coupled with loop extrusion (Nuebler et al., 2018), as the loss of cohesin in this model would results in microphases occurring only at large (∼500 kbp) length scales. To test this experimentally, we degraded RAD21 (Nishimura et al., 2009; Yesbolatova et al., 2020) using HCT116-Rad21-mAID2 cell line and performed ChromSTEM and live-cell PWS imaging of these cells in comparison to a vehicle treated control at 4 hr. As predicted and in contrast to expectation from existing chromatin polymer models, we found that (see Li, 2024) the majority of chromatin packing domains are retained (∼80% 62/78) with small changes in density (CVC 0.4 → 0.43), radius (84 → 89 nm), and (2.61 → 2.60). At the level of the heterogeneity of chromatin states observed in live cells, we performed live-cell PWS microscopy on cells with and without RAD21 depletion and find that it has a minimal impact on chromatin population diversity. Finally, we tested the prediction that local excluded volumes will predominantly determine the power-law geometry of chromatin within the nucleus. As observed on ChromSTEM, we find that the local volume concentrations will non-linearly relate to the scaling behavior of the chromatin polymer while being minimally influenced by the change in α (Figure 10).

Human cell line U2OS cells (ATCC, #HTB-96) used for experimental validation of the model were cultured in McCoy’s 5A Modified Medium (Thermo Fisher Scientific, #16600-082) supplemented with 10% fetal bovine serum (FBS) (Thermo Fisher Scientific, #16000-044) and 100 µg/ml penicillin–streptomycin antibiotics (Thermo Fisher Scientific, #15140-122). Human cell line A549 cells (ATCC, #CCL-185) used for experimental validation of the model were cultured in Dulbecco’s modified Eagle’s medium (Thermo Fisher Scientific, #11965092) supplemented with 10% FBS (Thermo Fisher Scientific, #16000-044) and 100 µg/ml penicillin–streptomycin antibiotics (Thermo Fisher Scientific, #15140-122). Experiments were performed on cells from passages 5 to 10. All cells were maintained under recommended conditions at 37°C and 5% CO₂. Cells were verified to have no detectable mycoplasma contamination (ATCC, #30-1012K) prior to starting experiments.

Prior to imaging, cells were cultured in 35 mm glass-bottom Petri dishes. All cells were allowed a minimum of 24 hr to re-adhere and recover from trypsin-induced detachment. PWS imaging was performed when the surface confluence of the dish was approximately 70%.

The PWS optical instrument consists of a commercial inverted microscope (Leica, DMIRB) equipped with a broad-spectrum white light LED source (Xcite-120 light-emitting diode lamp, Excelitas), ×63 oil immersion objective (Leica HCX PL APO, NA1.4 or 0.6), long pass filter (Semrock, BLP01-405R-25), and Hamamatsu Image-EM CCD camera C9100-13 coupled to an LCTF (CRi VariSpec). Live cells were imaged and maintained under physiological conditions (37°C and 5% CO₂) using a stage top incubator (In Vivo Scientific, Stage Top Systems). Briefly, PWS directly measures the variations in spectral light interference that results from internal light scattering within the cell, due to heterogeneities in chromatin density, with sensitivity to length scales between 20 and 300 nm (Li et al., 2021). Variations in the refractive index distribution are characterized by the mass scaling (chromatin packing scaling) parameter, D. A detailed description of these methods is reported in several publications (Subramanian et al., 2009; Almassalha et al., 2016; Gladstein et al., 2018; Eid et al., 2020).

Cell samples were prepared as reported in Li et al., 2022. Cells were first washed with Hank’s Balanced Salt Solution without calcium and magnesium (Thermo Fisher Scientific, #14170112) three times, 2 min each. Fixation, blocking, DNA staining and 3,3′-diaminobenzidine tetrahydrochloride (DAB) solutions were prepared with 0.1 M sodium cacodylate buffer (pH = 7.4). Cells were fixed with 2% paraformaldehyde, 2.5% glutaraldehyde, 2 mM calcium chloride for 5 min in room temperature and 1 hr on ice and all the following steps were performed on ice or in cold temperature unless otherwise specified. After fixation, cells were washed with 0.1 M sodium cacodylate buffer five times, 2 min each. Cells were then blocked with 10 mM glycine, 10 mM potassium cyanide for 15 min. Cells were stained with 10 µM DRAQ5, 0.1% Saponin for 10 min and washed with the blocking solution three times 5 min each. Cells were bathed in 2.5 mM DAB and exposed to 150 W Xenon Lamp with ×100 objective lens and a Cy5 filter for 7 min. Cells were washed with 0.1 M sodium cacodylate buffer five times, 2 min each, followed by staining with 2% osmium tetroxide, 1.5% potassium ferrocyanide, 2 mM calcium chloride, 0.15 M sodium cacodylate buffer for 30 min. After osmium staining, cells were washed with double distilled water five times, 2 min each and sequentially dehydrated with 30%, 50%, 70%, 85%, 95%, 100% twice, ethanol, 2 min each. Cells were then washed with 100% ethanol for 2 min and infiltrated with Durcupan ACM ethanol solutions (1:1 for 20 min, and 2:1 for 2 hr) at room temperature. Cells were then infiltrated with resin mixture for 1 hr, resin mixture with accelerator for 1 hr in 50°C dry oven and embedded in BEEM capsule with the resin mixture at 60°C dry oven for 48 hr.

Resin sections with thickness around 100 nm were prepared with a Leica UC7 ultramicrotome and a 35°C DiATOME diamond knife. The sections were collected on copper slot grids with carbon/Formvar film and 10 nm colloidal gold nanoparticles were deposited on both sides of the section as fiducial markers. HAADF(High-angle annular dark-field imaging) images collected by a 200-kV cFEG Hitachi HD2300 scanning transmission electron microscope. For each sample, projections were collected from −60 to +60°C with 2°C increments, along two roughly perpendicular axes.

Each projection series along one rotation axis was aligned with IMOD using gold nanoparticle fiducial markers. After image alignment, penalized maximum likelihood algorithm in Tomopy was used to reconstruct the images with 40 iterations. IMOD was used to combine tomograms from different rotation axis of the same sample.

The chromatin domains were identified using FIJI. 2D chromatin density distributions were obtained by re-projection of the tomogram along z-axis, followed by Gaussian filtering with 5 pixels radius and CLAHE contrast enhancements with block size of 120 pixels. Chromatin domain centers were selected as the local maxima of chromatin density.

To evaluate the size of a domain, two properties were analyzed for each domain, which are the mass scaling properties and radial volume chromatin concentration (CVC). For mass scaling, multiple mass scaling curves were sampled by using pixels (a 11-pixel × 11-pixel window) around the center of an identified domain and they were averaged by the weight of the pixel values of the selected center pixel. A size of domain is defined by the length scale that the domain meets any of the following three criteria: (1) it deviates from the power-law mass scaling relationship M(r)∝rD by 5%; (2) the local fitting of D reaches 3; (3) the radial CVC reaches a local minimum and begins to increase for longer length scale.

GraphPad Prism 10.0.0 was used to make the violin plots in Figures 7C and 8C. The violin plots are represented as individual data points, with lines at the median and quartiles.